Rotational Motion

Learn how to describe and measure rotational motion.

Learn how torque changes rotational velocity.

Define center of mass and the conditions for equilibrium.

Chapter

8

In this chapter you will:

Table of Contents

Chapter 8: Rotational Motion

Section 8.1: Describing Rotational Motion

Section 8.2: Rotational Dynamics

Section 8.3: Equilibrium

Chapter

8

Assignments:

Read Chapter 8.

Study Guide 8 due before the Chapter Test.

HW 8.A: p.223: 72-77.

HW 8.B: p.224: 81,82,84. p.225: 91,97.

HW 8.C: Handout

Describing Rotational Motion

Describe angular displacement.

Calculate angular velocity.

Calculate angular acceleration.

Solve problems involving rotational motion.

In this section you will:

Section

8.1

One complete revolution is equal to 2π radians, so

360 degrees = 2 π radians

Describing Rotational Motion

A fraction of one revolution can be measured in grads, degrees, or radians.

Describing Rotational Motion

Section

8.1

A grad is 1/400 of a revolution.

A degree is 1/360 of a revolution.

The ___________________ is defined as ½ π of a revolution. The abbreviation of radian is ‘rad’. The distance around the circle is 2πr.

Length = d

For rotation through an angle, θ, a point at a distance, r, from the

center moves a distance given by _________________________.

The Greek letter theta, θ, is used to represent the angle of revolution.

The counterclockwise rotation is designated as positive, while clockwise is negative.

As an object rotates, the change in the angle is

called_______________

Angular Displacement

Section

8.1

Describing Rotational Motion

Velocity is displacement divided by the time taken to make the displacement.

The of an object is angular displacement divided by the time required to make the displacement.

Angular Velocity

Section

8.1

The angular velocity of an object is given by:

Here angular velocity is represented by the Greek letter omega, ω.

The angular velocity is equal to the angular displacement divided by the time required to make the rotation.

Describing Rotational Motion

For Earth, ωE = (2π rad)/(24.0 h)(3600 s/h) = 7.27×10─5 rad/s.

Angular Velocity

Section

8.1

In the same way that counterclockwise rotation produces positive angular displacement, it also results in positive angular velocity.

If an object’s angular velocity is ω, then the linear velocity of a point a distance, r, from the axis of rotation is given by

The speed at which an object on Earth’s equator moves as a result of Earth’s rotation is given by v = r ω = (6.38×106 m) (7.27×10─5 rad/s) = 464 m/s.

Earth is an example of a rotating, rigid object. Even though different points on Earth rotate different distances in each revolution, all points rotate through the same angle.

Describing Rotational Motion

is defined as the change in angular velocity divided by the time required to make that change.

Angular Acceleration

Section

8.1

Angular acceleration is measured in .

If the change in angular velocity is positive, then the angular acceleration also is positive.

The angular acceleration, α, is represented by the following

equation:

Describing Rotational Motion

A summary of linear and angular relationships.

Angular Acceleration

Section

8.1

p.200: Practice Problems: 1,2. Section Review: 5,7-10.

HW 8.A: p.223: 72-77.

Section Check

What is the angular velocity of the minute hand of a clock?

Question 1

Section

8.1

A.

B.

C.

D.

π rad/s

60

π rad/s

30

π rad/s

π rad/s

90

Section Check

When a machine is switched on, the angular velocity of the motor increases by 10 rad/s for the first 10 seconds before it starts rotating with full speed. What is the angular acceleration of the machine in the first 10 seconds?

Question 2

Section

8.1

A. π rad/s2

B. 1 rad/s2

C. 100π rad/s2

D. 100 rad/s2

Section Check

When a fan performing 10 revolutions per second is switched off, it comes to rest after 10 seconds. Calculate the average angular acceleration of the fan after it was switched off.

Question 3

Section

8.1

A. 1 rad/s2

B. 2π rad/s2

C. π rad/s2

D. 10 rad/s2